LMFDB - Embedded newform 4020.2.q.l.3781.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.1
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.l.841.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(-2.18326 - 3.78152i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(-2.18326 - 3.78152i) q^{7} +1.00000 q^{9} +(-0.774215 - 1.34098i) q^{11} +(2.02478 - 3.50702i) q^{13} +1.00000 q^{15} +(1.99263 - 3.45134i) q^{17} +(2.00975 - 3.48099i) q^{19} +(2.18326 + 3.78152i) q^{21} +(2.40559 - 4.16660i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.387293 + 0.670812i) q^{29} +(-0.951794 - 1.64856i) q^{31} +(0.774215 + 1.34098i) q^{33} +(2.18326 + 3.78152i) q^{35} +(2.51829 - 4.36181i) q^{37} +(-2.02478 + 3.50702i) q^{39} +(2.44093 + 4.22781i) q^{41} +3.63465 q^{43} -1.00000 q^{45} +(3.40947 + 5.90538i) q^{47} +(-6.03327 + 10.4499i) q^{49} +(-1.99263 + 3.45134i) q^{51} +2.93977 q^{53} +(0.774215 + 1.34098i) q^{55} +(-2.00975 + 3.48099i) q^{57} -9.02740 q^{59} +(2.44868 - 4.24123i) q^{61} +(-2.18326 - 3.78152i) q^{63} +(-2.02478 + 3.50702i) q^{65} +(8.16914 + 0.514996i) q^{67} +(-2.40559 + 4.16660i) q^{69} +(-5.16336 - 8.94320i) q^{71} +(1.95853 - 3.39227i) q^{73} -1.00000 q^{75} +(-3.38063 + 5.85542i) q^{77} +(-5.84670 - 10.1268i) q^{79} +1.00000 q^{81} +(5.02913 - 8.71071i) q^{83} +(-1.99263 + 3.45134i) q^{85} +(-0.387293 - 0.670812i) q^{87} +11.9973 q^{89} -17.6825 q^{91} +(0.951794 + 1.64856i) q^{93} +(-2.00975 + 3.48099i) q^{95} +(0.0931549 - 0.161349i) q^{97} +(-0.774215 - 1.34098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.18326	−	3.78152i	−0.825196	−	1.42928i	−0.901770	−	0.432217i	$-0.857732\pi$
$7$	−2.18326	−	3.78152i	−0.825196	−	1.42928i	0.0765741	−	0.997064i	$-0.475602\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.774215	−	1.34098i	−0.233435	−	0.404321i	0.725382	−	0.688347i	$-0.241663\pi$
$11$	−0.774215	−	1.34098i	−0.233435	−	0.404321i	−0.958817	+	0.284026i	$0.908330\pi$
$12$		0			0
$13$	2.02478	−	3.50702i	0.561573	−	0.972673i	−0.435786	−	0.900050i	$-0.643530\pi$
$13$	2.02478	−	3.50702i	0.561573	−	0.972673i	0.997359	−	0.0726231i	$-0.0231370\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.99263	−	3.45134i	0.483284	−	0.837072i	−0.516532	−	0.856268i	$-0.672777\pi$
$17$	1.99263	−	3.45134i	0.483284	−	0.837072i	0.999816	+	0.0191959i	$0.00611063\pi$
$18$		0			0
$19$	2.00975	−	3.48099i	0.461069	−	0.798595i	−0.537946	−	0.842980i	$-0.680799\pi$
$19$	2.00975	−	3.48099i	0.461069	−	0.798595i	0.999015	+	0.0443849i	$0.0141328\pi$
$20$		0			0
$21$	2.18326	+	3.78152i	0.476427	+	0.825196i
$22$		0			0
$23$	2.40559	−	4.16660i	0.501599	−	0.868796i	−0.498399	−	0.866948i	$-0.666078\pi$
$23$	2.40559	−	4.16660i	0.501599	−	0.868796i	0.999998	−	0.00184784i	$-0.000588185\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.387293	+	0.670812i	0.0719186	+	0.124567i	0.899742	−	0.436422i	$-0.143754\pi$
$29$	0.387293	+	0.670812i	0.0719186	+	0.124567i	−0.827824	+	0.560989i	$0.810421\pi$
$30$		0			0
$31$	−0.951794	−	1.64856i	−0.170947	−	0.296089i	0.767804	−	0.640685i	$-0.221349\pi$
$31$	−0.951794	−	1.64856i	−0.170947	−	0.296089i	−0.938751	+	0.344595i	$0.888016\pi$
$32$		0			0
$33$	0.774215	+	1.34098i	0.134774	+	0.233435i
$34$		0			0
$35$	2.18326	+	3.78152i	0.369039	+	0.639194i
$36$		0			0
$37$	2.51829	−	4.36181i	0.414005	−	0.717077i	−0.581319	−	0.813676i	$-0.697463\pi$
$37$	2.51829	−	4.36181i	0.414005	−	0.717077i	0.995323	+	0.0965986i	$0.0307963\pi$
$38$		0			0
$39$	−2.02478	+	3.50702i	−0.324224	+	0.561573i
$40$		0			0
$41$	2.44093	+	4.22781i	0.381209	+	0.660273i	0.991235	−	0.132108i	$-0.0421746\pi$
$41$	2.44093	+	4.22781i	0.381209	+	0.660273i	−0.610027	+	0.792381i	$0.708841\pi$
$42$		0			0
$43$	3.63465			0.554278			0.277139	−	0.960830i	$-0.410614\pi$
$43$	3.63465			0.554278			0.277139	+	0.960830i	$0.410614\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	3.40947	+	5.90538i	0.497323	+	0.861388i	0.999995	−	0.00308877i	$-0.000983187\pi$
$47$	3.40947	+	5.90538i	0.497323	+	0.861388i	−0.502673	+	0.864477i	$0.667650\pi$
$48$		0			0
$49$	−6.03327	+	10.4499i	−0.861896	+	1.49285i
$50$		0			0
$51$	−1.99263	+	3.45134i	−0.279024	+	0.483284i
$52$		0			0
$53$	2.93977			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$53$	2.93977			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$54$		0			0
$55$	0.774215	+	1.34098i	0.104395	+	0.180818i
$56$		0			0
$57$	−2.00975	+	3.48099i	−0.266198	+	0.461069i
$58$		0			0
$59$	−9.02740			−1.17527			−0.587633	−	0.809127i	$-0.699940\pi$
$59$	−9.02740			−1.17527			−0.587633	+	0.809127i	$0.699940\pi$
$60$		0			0
$61$	2.44868	−	4.24123i	0.313521	−	0.543034i	−0.665601	−	0.746308i	$-0.731825\pi$
$61$	2.44868	−	4.24123i	0.313521	−	0.543034i	0.979122	+	0.203274i	$0.0651581\pi$
$62$		0			0
$63$	−2.18326	−	3.78152i	−0.275065	−	0.476427i
$64$		0			0
$65$	−2.02478	+	3.50702i	−0.251143	+	0.434993i
$66$		0			0
$67$	8.16914	+	0.514996i	0.998019	+	0.0629168i
$67$	8.16914	+	0.514996i	0.998019	+	0.0629168i
$68$		0			0
$69$	−2.40559	+	4.16660i	−0.289599	+	0.501599i
$70$		0			0
$71$	−5.16336	−	8.94320i	−0.612778	−	1.06136i	−0.990770	−	0.135554i	$-0.956719\pi$
$71$	−5.16336	−	8.94320i	−0.612778	−	1.06136i	0.377992	−	0.925809i	$-0.376615\pi$
$72$		0			0
$73$	1.95853	−	3.39227i	0.229228	−	0.397035i	−0.728351	−	0.685204i	$-0.759713\pi$
$73$	1.95853	−	3.39227i	0.229228	−	0.397035i	0.957580	+	0.288169i	$0.0930464\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−3.38063	+	5.85542i	−0.385259	+	0.667287i
$78$		0			0
$79$	−5.84670	−	10.1268i	−0.657805	−	1.13935i	−0.981183	−	0.193082i	$-0.938152\pi$
$79$	−5.84670	−	10.1268i	−0.657805	−	1.13935i	0.323377	−	0.946270i	$-0.395182\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	5.02913	−	8.71071i	0.552019	−	0.956124i	−0.446110	−	0.894978i	$-0.647191\pi$
$83$	5.02913	−	8.71071i	0.552019	−	0.956124i	0.998129	−	0.0611463i	$-0.0194756\pi$
$84$		0			0
$85$	−1.99263	+	3.45134i	−0.216131	+	0.374350i
$86$		0			0
$87$	−0.387293	−	0.670812i	−0.0415222	−	0.0719186i
$88$		0			0
$89$	11.9973			1.27172			0.635858	−	0.771806i	$-0.280646\pi$
$89$	11.9973			1.27172			0.635858	+	0.771806i	$0.280646\pi$
$90$		0			0
$91$	−17.6825			−1.85363
$92$		0			0
$93$	0.951794	+	1.64856i	0.0986965	+	0.170947i
$94$		0			0
$95$	−2.00975	+	3.48099i	−0.206196	+	0.357142i
$96$		0			0
$97$	0.0931549	−	0.161349i	0.00945845	−	0.0163825i	−0.861257	−	0.508169i	$-0.830323\pi$
$97$	0.0931549	−	0.161349i	0.00945845	−	0.0163825i	0.870716	+	0.491786i	$0.163656\pi$
$98$		0			0
$99$	−0.774215	−	1.34098i	−0.0778116	−	0.134774i
$100$		0			0
$101$	3.32909	+	5.76615i	0.331257	+	0.573753i	0.982759	−	0.184894i	$-0.0591941\pi$
$101$	3.32909	+	5.76615i	0.331257	+	0.573753i	−0.651502	+	0.758647i	$0.725861\pi$
$102$		0			0
$103$	−2.77624	−	4.80859i	−0.273551	−	0.473805i	0.696217	−	0.717831i	$-0.254865\pi$
$103$	−2.77624	−	4.80859i	−0.273551	−	0.473805i	−0.969769	+	0.244026i	$0.921532\pi$
$104$		0			0
$105$	−2.18326	−	3.78152i	−0.213065	−	0.369039i
$106$		0			0
$107$	−6.51834			−0.630151			−0.315076	−	0.949067i	$-0.602030\pi$
$107$	−6.51834			−0.630151			−0.315076	+	0.949067i	$0.602030\pi$
$108$		0			0
$109$	−15.1705			−1.45307			−0.726533	−	0.687132i	$-0.758870\pi$
$109$	−15.1705			−1.45307			−0.726533	+	0.687132i	$0.758870\pi$
$110$		0			0
$111$	−2.51829	+	4.36181i	−0.239026	+	0.414005i
$112$		0			0
$113$	7.43521	+	12.8782i	0.699446	+	1.21148i	0.968659	+	0.248395i	$0.0799032\pi$
$113$	7.43521	+	12.8782i	0.699446	+	1.21148i	−0.269213	+	0.963081i	$0.586763\pi$
$114$		0			0
$115$	−2.40559	+	4.16660i	−0.224322	+	0.388537i
$116$		0			0
$117$	2.02478	−	3.50702i	0.187191	−	0.324224i
$118$		0			0
$119$	−17.4017			−1.59521
$120$		0			0
$121$	4.30118	−	7.44986i	0.391016	−	0.677260i
$122$		0			0
$123$	−2.44093	−	4.22781i	−0.220091	−	0.381209i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.37459	+	4.11291i	0.210711	+	0.364962i	0.951937	−	0.306293i	$-0.0990888\pi$
$127$	2.37459	+	4.11291i	0.210711	+	0.364962i	−0.741226	+	0.671255i	$0.765755\pi$
$128$		0			0
$129$	−3.63465			−0.320013
$130$		0			0
$131$	−0.249267			−0.0217785			−0.0108893	−	0.999941i	$-0.503466\pi$
$131$	−0.249267			−0.0217785			−0.0108893	+	0.999941i	$0.503466\pi$
$132$		0			0
$133$	−17.5513			−1.52189
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−16.4329			−1.40396			−0.701980	−	0.712197i	$-0.747700\pi$
$137$	−16.4329			−1.40396			−0.701980	+	0.712197i	$0.747700\pi$
$138$		0			0
$139$	−8.61090			−0.730367			−0.365184	−	0.930936i	$-0.618994\pi$
$139$	−8.61090			−0.730367			−0.365184	+	0.930936i	$0.618994\pi$
$140$		0			0
$141$	−3.40947	−	5.90538i	−0.287129	−	0.497323i
$142$		0			0
$143$	−6.27047			−0.524363
$144$		0			0
$145$	−0.387293	−	0.670812i	−0.0321630	−	0.0557079i
$146$		0			0
$147$	6.03327	−	10.4499i	0.497616	−	0.861896i
$148$		0			0
$149$	12.9091			1.05755			0.528777	−	0.848761i	$-0.322651\pi$
$149$	12.9091			1.05755			0.528777	+	0.848761i	$0.322651\pi$
$150$		0			0
$151$	1.79380	−	3.10695i	0.145977	−	0.252840i	−0.783760	−	0.621064i	$-0.786701\pi$
$151$	1.79380	−	3.10695i	0.145977	−	0.252840i	0.929737	+	0.368224i	$0.120034\pi$
$152$		0			0
$153$	1.99263	−	3.45134i	0.161095	−	0.279024i
$154$		0			0
$155$	0.951794	+	1.64856i	0.0764500	+	0.132415i
$156$		0			0
$157$	0.0871390	−	0.150929i	0.00695445	−	0.0120455i	−0.862527	−	0.506011i	$-0.831120\pi$
$157$	0.0871390	−	0.150929i	0.00695445	−	0.0120455i	0.869482	+	0.493965i	$0.164453\pi$
$158$		0			0
$159$	−2.93977			−0.233139
$160$		0			0
$161$	−21.0081			−1.65567
$162$		0			0
$163$	1.82908	+	3.16805i	0.143264	+	0.248141i	0.928724	−	0.370772i	$-0.120907\pi$
$163$	1.82908	+	3.16805i	0.143264	+	0.248141i	−0.785460	+	0.618913i	$0.787573\pi$
$164$		0			0
$165$	−0.774215	−	1.34098i	−0.0602726	−	0.104395i
$166$		0			0
$167$	−6.18346	−	10.7101i	−0.478491	−	0.828770i	0.521205	−	0.853431i	$-0.325483\pi$
$167$	−6.18346	−	10.7101i	−0.478491	−	0.828770i	−0.999696	+	0.0246611i	$0.992149\pi$
$168$		0			0
$169$	−1.69948	−	2.94358i	−0.130729	−	0.226429i
$170$		0			0
$171$	2.00975	−	3.48099i	0.153690	−	0.266198i
$172$		0			0
$173$	−5.13800	+	8.89928i	−0.390635	+	0.676600i	−0.992533	−	0.121973i	$-0.961078\pi$
$173$	−5.13800	+	8.89928i	−0.390635	+	0.676600i	0.601898	+	0.798573i	$0.294411\pi$
$174$		0			0
$175$	−2.18326	−	3.78152i	−0.165039	−	0.285856i
$176$		0			0
$177$	9.02740			0.678541
$178$		0			0
$179$	4.67334			0.349301			0.174651	−	0.984630i	$-0.444120\pi$
$179$	4.67334			0.349301			0.174651	+	0.984630i	$0.444120\pi$
$180$		0			0
$181$	−8.86171	−	15.3489i	−0.658685	−	1.14088i	−0.980956	−	0.194229i	$-0.937779\pi$
$181$	−8.86171	−	15.3489i	−0.658685	−	1.14088i	0.322271	−	0.946648i	$-0.395554\pi$
$182$		0			0
$183$	−2.44868	+	4.24123i	−0.181011	+	0.313521i
$184$		0			0
$185$	−2.51829	+	4.36181i	−0.185149	+	0.320687i
$186$		0			0
$187$	−6.17090			−0.451261
$188$		0			0
$189$	2.18326	+	3.78152i	0.158809	+	0.275065i
$190$		0			0
$191$	2.71018	−	4.69417i	0.196102	−	0.339658i	−0.751159	−	0.660121i	$-0.770505\pi$
$191$	2.71018	−	4.69417i	0.196102	−	0.339658i	0.947261	+	0.320463i	$0.103838\pi$
$192$		0			0
$193$	9.93928			0.715445			0.357723	−	0.933828i	$-0.383553\pi$
$193$	9.93928			0.715445			0.357723	+	0.933828i	$0.383553\pi$
$194$		0			0
$195$	2.02478	−	3.50702i	0.144998	−	0.251143i
$196$		0			0
$197$	0.490545	+	0.849650i	0.0349499	+	0.0605350i	0.882971	−	0.469427i	$-0.155539\pi$
$197$	0.490545	+	0.849650i	0.0349499	+	0.0605350i	−0.848021	+	0.529962i	$0.822206\pi$
$198$		0			0
$199$	−1.34262	+	2.32548i	−0.0951756	+	0.164849i	−0.909682	−	0.415306i	$-0.863675\pi$
$199$	−1.34262	+	2.32548i	−0.0951756	+	0.164849i	0.814506	+	0.580155i	$0.197008\pi$
$200$		0			0
$201$	−8.16914	−	0.514996i	−0.576206	−	0.0363250i
$202$		0			0
$203$	1.69113	−	2.92912i	0.118694	−	0.205584i
$204$		0			0
$205$	−2.44093	−	4.22781i	−0.170482	−	0.295283i
$206$		0			0
$207$	2.40559	−	4.16660i	0.167200	−	0.289599i
$208$		0			0
$209$	−6.22392			−0.430518
$210$		0			0
$211$	−3.83190	+	6.63704i	−0.263799	+	0.456913i	−0.967248	−	0.253833i	$-0.918309\pi$
$211$	−3.83190	+	6.63704i	−0.263799	+	0.456913i	0.703450	+	0.710745i	$0.251642\pi$
$212$		0			0
$213$	5.16336	+	8.94320i	0.353788	+	0.612778i
$214$		0			0
$215$	−3.63465			−0.247881
$216$		0			0
$217$	−4.15603	+	7.19846i	−0.282130	+	0.488663i
$218$		0			0
$219$	−1.95853	+	3.39227i	−0.132345	+	0.229228i
$220$		0			0
$221$	−8.06928	−	13.9764i	−0.542798	−	0.940154i
$222$		0			0
$223$	21.2812			1.42510			0.712549	−	0.701623i	$-0.247541\pi$
$223$	21.2812			1.42510			0.712549	+	0.701623i	$0.247541\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−7.97874	−	13.8196i	−0.529567	−	0.917238i	−0.999405	−	0.0344849i	$-0.989021\pi$
$227$	−7.97874	−	13.8196i	−0.529567	−	0.917238i	0.469838	−	0.882753i	$-0.344312\pi$
$228$		0			0
$229$	−5.32882	+	9.22978i	−0.352138	+	0.609921i	−0.986624	−	0.163013i	$-0.947879\pi$
$229$	−5.32882	+	9.22978i	−0.352138	+	0.609921i	0.634486	+	0.772935i	$0.281212\pi$
$230$		0			0
$231$	3.38063	−	5.85542i	0.222429	−	0.385259i
$232$		0			0
$233$	2.99402	+	5.18580i	0.196145	+	0.339733i	0.947275	−	0.320421i	$-0.103824\pi$
$233$	2.99402	+	5.18580i	0.196145	+	0.339733i	−0.751130	+	0.660154i	$0.770491\pi$
$234$		0			0
$235$	−3.40947	−	5.90538i	−0.222409	−	0.385224i
$236$		0			0
$237$	5.84670	+	10.1268i	0.379784	+	0.657805i
$238$		0			0
$239$	10.4991	+	18.1850i	0.679131	+	1.17629i	0.975243	+	0.221137i	$0.0709767\pi$
$239$	10.4991	+	18.1850i	0.679131	+	1.17629i	−0.296111	+	0.955153i	$0.595690\pi$
$240$		0			0
$241$	−13.6890			−0.881784			−0.440892	−	0.897560i	$-0.645338\pi$
$241$	−13.6890			−0.881784			−0.440892	+	0.897560i	$0.645338\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	6.03327	−	10.4499i	0.385451	−	0.667621i
$246$		0			0
$247$	−8.13862	−	14.0965i	−0.517848	−	0.896939i
$248$		0			0
$249$	−5.02913	+	8.71071i	−0.318708	+	0.552019i
$250$		0			0
$251$	2.93590	−	5.08513i	0.185313	−	0.320971i	−0.758369	−	0.651825i	$-0.774004\pi$
$251$	2.93590	−	5.08513i	0.185313	−	0.320971i	0.943682	+	0.330854i	$0.107337\pi$
$252$		0			0
$253$	−7.44977			−0.468363
$254$		0			0
$255$	1.99263	−	3.45134i	0.124783	−	0.216131i
$256$		0			0
$257$	2.40142	+	4.15939i	0.149797	+	0.259456i	0.931152	−	0.364631i	$-0.118805\pi$
$257$	2.40142	+	4.15939i	0.149797	+	0.259456i	−0.781356	+	0.624086i	$0.785471\pi$
$258$		0			0
$259$	−21.9924			−1.36654
$260$		0			0
$261$	0.387293	+	0.670812i	0.0239729	+	0.0415222i
$262$		0			0
$263$	8.03375			0.495382			0.247691	−	0.968839i	$-0.420328\pi$
$263$	8.03375			0.495382			0.247691	+	0.968839i	$0.420328\pi$
$264$		0			0
$265$	−2.93977			−0.180588
$266$		0			0
$267$	−11.9973			−0.734226
$268$		0			0
$269$	20.5623			1.25370			0.626851	−	0.779139i	$-0.284343\pi$
$269$	20.5623			1.25370			0.626851	+	0.779139i	$0.284343\pi$
$270$		0			0
$271$	−18.9461			−1.15089			−0.575445	−	0.817840i	$-0.695171\pi$
$271$	−18.9461			−1.15089			−0.575445	+	0.817840i	$0.695171\pi$
$272$		0			0
$273$	17.6825			1.07019
$274$		0			0
$275$	−0.774215	−	1.34098i	−0.0466869	−	0.0808641i
$276$		0			0
$277$	−18.4595			−1.10912			−0.554561	−	0.832143i	$-0.687114\pi$
$277$	−18.4595			−1.10912			−0.554561	+	0.832143i	$0.687114\pi$
$278$		0			0
$279$	−0.951794	−	1.64856i	−0.0569824	−	0.0986965i
$280$		0			0
$281$	1.81169	−	3.13794i	0.108076	−	0.187194i	−0.806915	−	0.590668i	$-0.798864\pi$
$281$	1.81169	−	3.13794i	0.108076	−	0.187194i	0.914991	+	0.403474i	$0.132198\pi$
$282$		0			0
$283$	−18.7679			−1.11564			−0.557818	−	0.829964i	$-0.688361\pi$
$283$	−18.7679			−1.11564			−0.557818	+	0.829964i	$0.688361\pi$
$284$		0			0
$285$	2.00975	−	3.48099i	0.119047	−	0.206196i
$286$		0			0
$287$	10.6584	−	18.4608i	0.629143	−	1.08971i
$288$		0			0
$289$	0.558854	+	0.967963i	0.0328737	+	0.0569390i
$290$		0			0
$291$	−0.0931549	+	0.161349i	−0.00546084	+	0.00945845i
$292$		0			0
$293$	14.6838			0.857839			0.428920	−	0.903343i	$-0.358894\pi$
$293$	14.6838			0.857839			0.428920	+	0.903343i	$0.358894\pi$
$294$		0			0
$295$	9.02740			0.525595
$296$		0			0
$297$	0.774215	+	1.34098i	0.0449245	+	0.0778116i
$298$		0			0
$299$	−9.74157	−	16.8729i	−0.563370	−	0.975785i
$300$		0			0
$301$	−7.93538	−	13.7445i	−0.457388	−	0.792219i
$302$		0			0
$303$	−3.32909	−	5.76615i	−0.191251	−	0.331257i
$304$		0			0
$305$	−2.44868	+	4.24123i	−0.140211	+	0.242852i
$306$		0			0
$307$	−11.8768	+	20.5711i	−0.677842	+	1.17406i	0.297787	+	0.954632i	$0.403752\pi$
$307$	−11.8768	+	20.5711i	−0.677842	+	1.17406i	−0.975629	+	0.219425i	$0.929582\pi$
$308$		0			0
$309$	2.77624	+	4.80859i	0.157935	+	0.273551i
$310$		0			0
$311$	−1.63955			−0.0929704			−0.0464852	−	0.998919i	$-0.514802\pi$
$311$	−1.63955			−0.0929704			−0.0464852	+	0.998919i	$0.514802\pi$
$312$		0			0
$313$	−1.62336			−0.0917576			−0.0458788	−	0.998947i	$-0.514609\pi$
$313$	−1.62336			−0.0917576			−0.0458788	+	0.998947i	$0.514609\pi$
$314$		0			0
$315$	2.18326	+	3.78152i	0.123013	+	0.213065i
$316$		0			0
$317$	−8.96536	+	15.5285i	−0.503545	+	0.872165i	0.496447	+	0.868067i	$0.334638\pi$
$317$	−8.96536	+	15.5285i	−0.503545	+	0.872165i	−0.999992	+	0.00409784i	$0.998696\pi$
$318$		0			0
$319$	0.599697	−	1.03871i	0.0335766	−	0.0581563i
$320$		0			0
$321$	6.51834			0.363818
$322$		0			0
$323$	−8.00938	−	13.8727i	−0.445654	−	0.771896i
$324$		0			0
$325$	2.02478	−	3.50702i	0.112315	−	0.194535i
$326$		0			0
$327$	15.1705			0.838928
$328$		0			0
$329$	14.8875	−	25.7860i	0.820777	−	1.42163i
$330$		0			0
$331$	−3.99055	−	6.91184i	−0.219341	−	0.379909i	0.735266	−	0.677779i	$-0.237057\pi$
$331$	−3.99055	−	6.91184i	−0.219341	−	0.379909i	−0.954607	+	0.297870i	$0.903724\pi$
$332$		0			0
$333$	2.51829	−	4.36181i	0.138002	−	0.239026i
$334$		0			0
$335$	−8.16914	−	0.514996i	−0.446328	−	0.0281372i
$336$		0			0
$337$	6.30931	−	10.9280i	0.343690	−	0.595289i	−0.641425	−	0.767186i	$-0.721656\pi$
$337$	6.30931	−	10.9280i	0.343690	−	0.595289i	0.985115	+	0.171897i	$0.0549897\pi$
$338$		0			0
$339$	−7.43521	−	12.8782i	−0.403825	−	0.699446i
$340$		0			0
$341$	−1.47379	+	2.55267i	−0.0798101	+	0.138235i
$342$		0			0
$343$	22.1232			1.19454
$344$		0			0
$345$	2.40559	−	4.16660i	0.129512	−	0.224322i
$346$		0			0
$347$	7.59815	+	13.1604i	0.407890	+	0.706487i	0.994653	−	0.103272i	$-0.0329313\pi$
$347$	7.59815	+	13.1604i	0.407890	+	0.706487i	−0.586763	+	0.809759i	$0.699598\pi$
$348$		0			0
$349$	−33.3604			−1.78574			−0.892871	−	0.450312i	$-0.851313\pi$
$349$	−33.3604			−1.78574			−0.892871	+	0.450312i	$0.851313\pi$
$350$		0			0
$351$	−2.02478	+	3.50702i	−0.108075	+	0.187191i
$352$		0			0
$353$	−2.95901	+	5.12516i	−0.157492	+	0.272785i	−0.933964	−	0.357368i	$-0.883674\pi$
$353$	−2.95901	+	5.12516i	−0.157492	+	0.272785i	0.776471	+	0.630152i	$0.217008\pi$
$354$		0			0
$355$	5.16336	+	8.94320i	0.274043	+	0.474656i
$356$		0			0
$357$	17.4017			0.920997
$358$		0			0
$359$	−6.33249			−0.334216			−0.167108	−	0.985939i	$-0.553443\pi$
$359$	−6.33249			−0.334216			−0.167108	+	0.985939i	$0.553443\pi$
$360$		0			0
$361$	1.42179	+	2.46261i	0.0748311	+	0.129611i
$362$		0			0
$363$	−4.30118	+	7.44986i	−0.225753	+	0.391016i
$364$		0			0
$365$	−1.95853	+	3.39227i	−0.102514	+	0.177560i
$366$		0			0
$367$	9.07721	+	15.7222i	0.473826	+	0.820691i	0.999551	−	0.0299636i	$-0.00953913\pi$
$367$	9.07721	+	15.7222i	0.473826	+	0.820691i	−0.525725	+	0.850655i	$0.676206\pi$
$368$		0			0
$369$	2.44093	+	4.22781i	0.127070	+	0.220091i
$370$		0			0
$371$	−6.41828	−	11.1168i	−0.333221	−	0.577155i
$372$		0			0
$373$	−9.51926	−	16.4878i	−0.492889	−	0.853708i	0.507078	−	0.861900i	$-0.330726\pi$
$373$	−9.51926	−	16.4878i	−0.492889	−	0.853708i	−0.999966	+	0.00819205i	$0.997392\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	3.13674			0.161550
$378$		0			0
$379$	−9.12012	+	15.7965i	−0.468469	+	0.811413i	−0.999351	−	0.0360336i	$-0.988528\pi$
$379$	−9.12012	+	15.7965i	−0.468469	+	0.811413i	0.530881	+	0.847446i	$0.321861\pi$
$380$		0			0
$381$	−2.37459	−	4.11291i	−0.121654	−	0.210711i
$382$		0			0
$383$	6.06204	−	10.4998i	0.309756	−	0.536513i	−0.668553	−	0.743665i	$-0.733086\pi$
$383$	6.06204	−	10.4998i	0.309756	−	0.536513i	0.978309	+	0.207152i	$0.0664193\pi$
$384$		0			0
$385$	3.38063	−	5.85542i	0.172293	−	0.298420i
$386$		0			0
$387$	3.63465			0.184759
$388$		0			0
$389$	9.09748	−	15.7573i	0.461261	−	0.798927i	−0.537763	−	0.843096i	$-0.680731\pi$
$389$	9.09748	−	15.7573i	0.461261	−	0.798927i	0.999024	+	0.0441689i	$0.0140640\pi$
$390$		0			0
$391$	−9.58689	−	16.6050i	−0.484830	−	0.839750i
$392$		0			0
$393$	0.249267			0.0125739
$394$		0			0
$395$	5.84670	+	10.1268i	0.294179	+	0.509534i
$396$		0			0
$397$	16.0728			0.806670			0.403335	−	0.915052i	$-0.367851\pi$
$397$	16.0728			0.806670			0.403335	+	0.915052i	$0.367851\pi$
$398$		0			0
$399$	17.5513			0.878662
$400$		0			0
$401$	−20.4963			−1.02354			−0.511769	−	0.859123i	$-0.671010\pi$
$401$	−20.4963			−1.02354			−0.511769	+	0.859123i	$0.671010\pi$
$402$		0			0
$403$	−7.70870			−0.383998
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−7.79880			−0.386572
$408$		0			0
$409$	11.0692	+	19.1725i	0.547338	+	0.948017i	0.998456	+	0.0555529i	$0.0176921\pi$
$409$	11.0692	+	19.1725i	0.547338	+	0.948017i	−0.451118	+	0.892464i	$0.648975\pi$
$410$		0			0
$411$	16.4329			0.810576
$412$		0			0
$413$	19.7092	+	34.1373i	0.969825	+	1.67979i
$414$		0			0
$415$	−5.02913	+	8.71071i	−0.246870	+	0.427592i
$416$		0			0
$417$	8.61090			0.421678
$418$		0			0
$419$	16.4101	−	28.4232i	0.801688	−	1.38856i	−0.116817	−	0.993153i	$-0.537269\pi$
$419$	16.4101	−	28.4232i	0.801688	−	1.38856i	0.918505	−	0.395410i	$-0.129398\pi$
$420$		0			0
$421$	−18.7572	+	32.4884i	−0.914169	+	1.58339i	−0.106055	+	0.994360i	$0.533822\pi$
$421$	−18.7572	+	32.4884i	−0.914169	+	1.58339i	−0.808114	+	0.589027i	$0.799511\pi$
$422$		0			0
$423$	3.40947	+	5.90538i	0.165774	+	0.287129i
$424$		0			0
$425$	1.99263	−	3.45134i	0.0966567	−	0.167414i
$426$		0			0
$427$	−21.3844			−1.03486
$428$		0			0
$429$	6.27047			0.302741
$430$		0			0
$431$	−3.63745	−	6.30024i	−0.175210	−	0.303472i	0.765024	−	0.644002i	$-0.222727\pi$
$431$	−3.63745	−	6.30024i	−0.175210	−	0.303472i	−0.940234	+	0.340530i	$0.889394\pi$
$432$		0			0
$433$	13.2770	+	22.9965i	0.638053	+	1.10514i	0.985859	+	0.167574i	$0.0535934\pi$
$433$	13.2770	+	22.9965i	0.638053	+	1.10514i	−0.347806	+	0.937567i	$0.613073\pi$
$434$		0			0
$435$	0.387293	+	0.670812i	0.0185693	+	0.0321630i
$436$		0			0
$437$	−9.66927	−	16.7477i	−0.462544	−	0.801149i
$438$		0			0
$439$	15.5882	−	26.9995i	0.743984	−	1.28862i	−0.206685	−	0.978408i	$-0.566267\pi$
$439$	15.5882	−	26.9995i	0.743984	−	1.28862i	0.950668	−	0.310210i	$-0.100399\pi$
$440$		0			0
$441$	−6.03327	+	10.4499i	−0.287299	+	0.497616i
$442$		0			0
$443$	6.32988	+	10.9637i	0.300742	+	0.520900i	0.976304	−	0.216403i	$-0.0694325\pi$
$443$	6.32988	+	10.9637i	0.300742	+	0.520900i	−0.675563	+	0.737303i	$0.736099\pi$
$444$		0			0
$445$	−11.9973			−0.568729
$446$		0			0
$447$	−12.9091			−0.610579
$448$		0			0
$449$	15.2507	+	26.4149i	0.719723	+	1.24660i	0.961110	+	0.276167i	$0.0890644\pi$
$449$	15.2507	+	26.4149i	0.719723	+	1.24660i	−0.241387	+	0.970429i	$0.577602\pi$
$450$		0			0
$451$	3.77960	−	6.54647i	0.177975	−	0.308261i
$452$		0			0
$453$	−1.79380	+	3.10695i	−0.0842799	+	0.145977i
$454$		0			0
$455$	17.6825			0.828969
$456$		0			0
$457$	−6.52501	−	11.3016i	−0.305227	−	0.528669i	0.672085	−	0.740474i	$-0.265399\pi$
$457$	−6.52501	−	11.3016i	−0.305227	−	0.528669i	−0.977312	+	0.211805i	$0.932066\pi$
$458$		0			0
$459$	−1.99263	+	3.45134i	−0.0930080	+	0.161095i
$460$		0			0
$461$	−39.5153			−1.84041			−0.920205	−	0.391437i	$-0.871978\pi$
$461$	−39.5153			−1.84041			−0.920205	+	0.391437i	$0.871978\pi$
$462$		0			0
$463$	4.44180	−	7.69342i	0.206428	−	0.357543i	−0.744159	−	0.668003i	$-0.767149\pi$
$463$	4.44180	−	7.69342i	0.206428	−	0.357543i	0.950587	+	0.310459i	$0.100483\pi$
$464$		0			0
$465$	−0.951794	−	1.64856i	−0.0441384	−	0.0764500i
$466$		0			0
$467$	−6.86479	+	11.8902i	−0.317664	+	0.550211i	−0.980000	−	0.198996i	$-0.936232\pi$
$467$	−6.86479	+	11.8902i	−0.317664	+	0.550211i	0.662336	+	0.749207i	$0.269565\pi$
$468$		0			0
$469$	−15.8879	−	32.0161i	−0.733635	−	1.47837i
$470$		0			0
$471$	−0.0871390	+	0.150929i	−0.00401515	+	0.00695445i
$472$		0			0
$473$	−2.81400	−	4.87399i	−0.129388	−	0.224106i
$474$		0			0
$475$	2.00975	−	3.48099i	0.0922138	−	0.159719i
$476$		0			0
$477$	2.93977			0.134603
$478$		0			0
$479$	2.55719	−	4.42919i	0.116841	−	0.202375i	−0.801673	−	0.597763i	$-0.796057\pi$
$479$	2.55719	−	4.42919i	0.116841	−	0.202375i	0.918514	+	0.395388i	$0.129390\pi$
$480$		0			0
$481$	−10.1980	−	17.6634i	−0.464988	−	0.805383i
$482$		0			0
$483$	21.0081			0.955902
$484$		0			0
$485$	−0.0931549	+	0.161349i	−0.00422995	+	0.00732648i
$486$		0			0
$487$	2.83885	−	4.91703i	0.128641	−	0.222812i	−0.794510	−	0.607252i	$-0.792272\pi$
$487$	2.83885	−	4.91703i	0.128641	−	0.222812i	0.923150	+	0.384440i	$0.125605\pi$
$488$		0			0
$489$	−1.82908	−	3.16805i	−0.0827137	−	0.143264i
$490$		0			0
$491$	1.42882			0.0644818			0.0322409	−	0.999480i	$-0.489736\pi$
$491$	1.42882			0.0644818			0.0322409	+	0.999480i	$0.489736\pi$
$492$		0			0
$493$	3.08693			0.139028
$494$		0			0
$495$	0.774215	+	1.34098i	0.0347984	+	0.0602726i
$496$		0			0
$497$	−22.5459	+	39.0507i	−1.01132	+	1.75166i
$498$		0			0
$499$	−15.5307	+	26.9000i	−0.695250	+	1.20421i	0.274847	+	0.961488i	$0.411373\pi$
$499$	−15.5307	+	26.9000i	−0.695250	+	1.20421i	−0.970096	+	0.242720i	$0.921960\pi$
$500$		0			0
$501$	6.18346	+	10.7101i	0.276257	+	0.478491i
$502$		0			0
$503$	9.56682	+	16.5702i	0.426563	+	0.738830i	0.996565	−	0.0828140i	$-0.0263908\pi$
$503$	9.56682	+	16.5702i	0.426563	+	0.738830i	−0.570002	+	0.821644i	$0.693057\pi$
$504$		0			0
$505$	−3.32909	−	5.76615i	−0.148142	−	0.256590i
$506$		0			0
$507$	1.69948	+	2.94358i	0.0754763	+	0.130729i
$508$		0			0
$509$	41.8386			1.85446			0.927232	−	0.374488i	$-0.122182\pi$
$509$	41.8386			1.85446			0.927232	+	0.374488i	$0.122182\pi$
$510$		0			0
$511$	−17.1039			−0.756633
$512$		0			0
$513$	−2.00975	+	3.48099i	−0.0887327	+	0.153690i
$514$		0			0
$515$	2.77624	+	4.80859i	0.122336	+	0.211892i
$516$		0			0
$517$	5.27933	−	9.14407i	0.232185	−	0.402156i
$518$		0			0
$519$	5.13800	−	8.89928i	0.225533	−	0.390635i
$520$		0			0
$521$	19.3936			0.849650			0.424825	−	0.905275i	$-0.360336\pi$
$521$	19.3936			0.849650			0.424825	+	0.905275i	$0.360336\pi$
$522$		0			0
$523$	13.9207	−	24.1113i	0.608708	−	1.05431i	−0.382746	−	0.923854i	$-0.625021\pi$
$523$	13.9207	−	24.1113i	0.608708	−	1.05431i	0.991454	−	0.130460i	$-0.0416453\pi$
$524$		0			0
$525$	2.18326	+	3.78152i	0.0952854	+	0.165039i
$526$		0			0
$527$	−7.58629			−0.330464
$528$		0			0
$529$	−0.0736910	−	0.127636i	−0.00320395	−	0.00554941i
$530$		0			0
$531$	−9.02740			−0.391756
$532$		0			0
$533$	19.7694			0.856306
$534$		0			0
$535$	6.51834			0.281812
$536$		0			0
$537$	−4.67334			−0.201669
$538$		0			0
$539$	18.6842			0.804785
$540$		0			0
$541$	−29.5874			−1.27206			−0.636030	−	0.771664i	$-0.719425\pi$
$541$	−29.5874			−1.27206			−0.636030	+	0.771664i	$0.719425\pi$
$542$		0			0
$543$	8.86171	+	15.3489i	0.380292	+	0.658685i
$544$		0			0
$545$	15.1705			0.649831
$546$		0			0
$547$	−13.5832	−	23.5268i	−0.580776	−	1.00593i	−0.995388	−	0.0959353i	$-0.969416\pi$
$547$	−13.5832	−	23.5268i	−0.580776	−	1.00593i	0.414611	−	0.909999i	$-0.363918\pi$
$548$		0			0
$549$	2.44868	−	4.24123i	0.104507	−	0.181011i
$550$		0			0
$551$	3.11345			0.132638
$552$		0			0
$553$	−25.5298	+	44.2188i	−1.08564	+	1.88038i
$554$		0			0
$555$	2.51829	−	4.36181i	0.106896	−	0.185149i
$556$		0			0
$557$	12.4280	+	21.5259i	0.526590	+	0.912081i	0.999520	+	0.0309809i	$0.00986310\pi$
$557$	12.4280	+	21.5259i	0.526590	+	0.912081i	−0.472930	+	0.881100i	$0.656804\pi$
$558$		0			0
$559$	7.35936	−	12.7468i	0.311268	−	0.539132i
$560$		0			0
$561$	6.17090			0.260535
$562$		0			0
$563$	−1.20628			−0.0508386			−0.0254193	−	0.999677i	$-0.508092\pi$
$563$	−1.20628			−0.0508386			−0.0254193	+	0.999677i	$0.508092\pi$
$564$		0			0
$565$	−7.43521	−	12.8782i	−0.312802	−	0.541789i
$566$		0			0
$567$	−2.18326	−	3.78152i	−0.0916884	−	0.158809i
$568$		0			0
$569$	17.0726	+	29.5706i	0.715721	+	1.23967i	0.962681	+	0.270639i	$0.0872351\pi$
$569$	17.0726	+	29.5706i	0.715721	+	1.23967i	−0.246960	+	0.969026i	$0.579432\pi$
$570$		0			0
$571$	18.5866	+	32.1929i	0.777824	+	1.34723i	0.933194	+	0.359374i	$0.117010\pi$
$571$	18.5866	+	32.1929i	0.777824	+	1.34723i	−0.155370	+	0.987856i	$0.549657\pi$
$572$		0			0
$573$	−2.71018	+	4.69417i	−0.113219	+	0.196102i
$574$		0			0
$575$	2.40559	−	4.16660i	0.100320	−	0.173759i
$576$		0			0
$577$	−19.9262	−	34.5131i	−0.829537	−	1.43680i	−0.898402	−	0.439175i	$-0.855271\pi$
$577$	−19.9262	−	34.5131i	−0.829537	−	1.43680i	0.0688642	−	0.997626i	$-0.478062\pi$
$578$		0			0
$579$	−9.93928			−0.413063
$580$		0			0
$581$	−43.9196			−1.82209
$582$		0			0
$583$	−2.27601	−	3.94217i	−0.0942628	−	0.163268i
$584$		0			0
$585$	−2.02478	+	3.50702i	−0.0837144	+	0.144998i
$586$		0			0
$587$	−14.0039	+	24.2554i	−0.578002	+	1.00113i	0.417706	+	0.908582i	$0.362834\pi$
$587$	−14.0039	+	24.2554i	−0.578002	+	1.00113i	−0.995708	+	0.0925471i	$0.970499\pi$
$588$		0			0
$589$	−7.65148			−0.315274
$590$		0			0
$591$	−0.490545	−	0.849650i	−0.0201783	−	0.0349499i
$592$		0			0
$593$	8.77482	−	15.1984i	0.360339	−	0.624125i	−0.627678	−	0.778473i	$-0.715994\pi$
$593$	8.77482	−	15.1984i	0.360339	−	0.624125i	0.988016	+	0.154348i	$0.0493278\pi$
$594$		0			0
$595$	17.4017			0.713402
$596$		0			0
$597$	1.34262	−	2.32548i	0.0549497	−	0.0951756i
$598$		0			0
$599$	11.4607	+	19.8505i	0.468270	+	0.811068i	0.999342	−	0.0362589i	$-0.0115441\pi$
$599$	11.4607	+	19.8505i	0.468270	+	0.811068i	−0.531072	+	0.847327i	$0.678211\pi$
$600$		0			0
$601$	−22.0783	+	38.2408i	−0.900594	+	1.55987i	−0.0738696	+	0.997268i	$0.523535\pi$
$601$	−22.0783	+	38.2408i	−0.900594	+	1.55987i	−0.826725	+	0.562607i	$0.809798\pi$
$602$		0			0
$603$	8.16914	+	0.514996i	0.332673	+	0.0209723i
$604$		0			0
$605$	−4.30118	+	7.44986i	−0.174868	+	0.302880i
$606$		0			0
$607$	3.48880	+	6.04278i	0.141606	+	0.245269i	0.928102	−	0.372327i	$-0.121440\pi$
$607$	3.48880	+	6.04278i	0.141606	+	0.245269i	−0.786496	+	0.617596i	$0.788107\pi$
$608$		0			0
$609$	−1.69113	+	2.92912i	−0.0685279	+	0.118694i
$610$		0			0
$611$	27.6137			1.11713
$612$		0			0
$613$	−3.67572	+	6.36653i	−0.148461	+	0.257142i	−0.930659	−	0.365888i	$-0.880765\pi$
$613$	−3.67572	+	6.36653i	−0.148461	+	0.257142i	0.782198	+	0.623030i	$0.214099\pi$
$614$		0			0
$615$	2.44093	+	4.22781i	0.0984276	+	0.170482i
$616$		0			0
$617$	−8.25619			−0.332382			−0.166191	−	0.986094i	$-0.553147\pi$
$617$	−8.25619			−0.332382			−0.166191	+	0.986094i	$0.553147\pi$
$618$		0			0
$619$	−0.414597	+	0.718102i	−0.0166640	+	0.0288630i	−0.874237	−	0.485499i	$-0.838638\pi$
$619$	−0.414597	+	0.718102i	−0.0166640	+	0.0288630i	0.857573	+	0.514362i	$0.171971\pi$
$620$		0			0
$621$	−2.40559	+	4.16660i	−0.0965329	+	0.167200i
$622$		0			0
$623$	−26.1934	−	45.3682i	−1.04941	−	1.81764i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	6.22392			0.248560
$628$		0			0
$629$	−10.0361	−	17.3830i	−0.400164	−	0.693104i
$630$		0			0
$631$	0.00462415	−	0.00800927i	0.000184085	−	0.000318844i	−0.865933	−	0.500159i	$-0.833275\pi$
$631$	0.00462415	−	0.00800927i	0.000184085	−	0.000318844i	0.866117	+	0.499841i	$0.166608\pi$
$632$		0			0
$633$	3.83190	−	6.63704i	0.152304	−	0.263799i
$634$		0			0
$635$	−2.37459	−	4.11291i	−0.0942328	−	0.163216i
$636$		0			0
$637$	24.4321	+	42.3176i	0.968035	+	1.67669i
$638$		0			0
$639$	−5.16336	−	8.94320i	−0.204259	−	0.353788i
$640$		0			0
$641$	1.80972	+	3.13454i	0.0714798	+	0.123807i	0.899550	−	0.436818i	$-0.143895\pi$
$641$	1.80972	+	3.13454i	0.0714798	+	0.123807i	−0.828070	+	0.560624i	$0.810561\pi$
$642$		0			0
$643$	45.7288			1.80337			0.901685	−	0.432394i	$-0.142331\pi$
$643$	45.7288			1.80337			0.901685	+	0.432394i	$0.142331\pi$
$644$		0			0
$645$	3.63465			0.143114
$646$		0			0
$647$	0.666592	−	1.15457i	0.0262064	−	0.0453909i	−0.852625	−	0.522524i	$-0.824991\pi$
$647$	0.666592	−	1.15457i	0.0262064	−	0.0453909i	0.878831	+	0.477133i	$0.158324\pi$
$648$		0			0
$649$	6.98915	+	12.1056i	0.274348	+	0.475185i
$650$		0			0
$651$	4.15603	−	7.19846i	0.162888	−	0.282130i
$652$		0			0
$653$	−8.15390	+	14.1230i	−0.319087	+	0.552674i	−0.980298	−	0.197526i	$-0.936709\pi$
$653$	−8.15390	+	14.1230i	−0.319087	+	0.552674i	0.661211	+	0.750200i	$0.270043\pi$
$654$		0			0
$655$	0.249267			0.00973966
$656$		0			0
$657$	1.95853	−	3.39227i	0.0764094	−	0.132345i
$658$		0			0
$659$	7.10050	+	12.2984i	0.276596	+	0.479079i	0.970537	−	0.240954i	$-0.0774602\pi$
$659$	7.10050	+	12.2984i	0.276596	+	0.479079i	−0.693940	+	0.720032i	$0.744127\pi$
$660$		0			0
$661$	7.32109			0.284757			0.142379	−	0.989812i	$-0.454525\pi$
$661$	7.32109			0.284757			0.142379	+	0.989812i	$0.454525\pi$
$662$		0			0
$663$	8.06928	+	13.9764i	0.313385	+	0.542798i
$664$		0			0
$665$	17.5513			0.680609
$666$		0			0
$667$	3.72667			0.144297
$668$		0			0
$669$	−21.2812			−0.822780
$670$		0			0
$671$	−7.58321			−0.292747
$672$		0			0
$673$	4.56848			0.176102			0.0880511	−	0.996116i	$-0.471936\pi$
$673$	4.56848			0.176102			0.0880511	+	0.996116i	$0.471936\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	12.3054	+	21.3136i	0.472936	+	0.819149i	0.999520	−	0.0309741i	$-0.00986095\pi$
$677$	12.3054	+	21.3136i	0.472936	+	0.819149i	−0.526584	+	0.850123i	$0.676528\pi$
$678$		0			0
$679$	−0.813527			−0.0312203
$680$		0			0
$681$	7.97874	+	13.8196i	0.305746	+	0.529567i
$682$		0			0
$683$	−11.0513	+	19.1414i	−0.422866	+	0.732425i	−0.996218	−	0.0868835i	$-0.972309\pi$
$683$	−11.0513	+	19.1414i	−0.422866	+	0.732425i	0.573353	+	0.819309i	$0.305643\pi$
$684$		0			0
$685$	16.4329			0.627870
$686$		0			0
$687$	5.32882	−	9.22978i	0.203307	−	0.352138i
$688$		0			0
$689$	5.95238	−	10.3098i	0.226768	−	0.392773i
$690$		0			0
$691$	2.43911	+	4.22466i	0.0927880	+	0.160713i	0.908683	−	0.417486i	$-0.137089\pi$
$691$	2.43911	+	4.22466i	0.0927880	+	0.160713i	−0.815895	+	0.578200i	$0.803755\pi$
$692$		0			0
$693$	−3.38063	+	5.85542i	−0.128420	+	0.222429i
$694$		0			0
$695$	8.61090			0.326630
$696$		0			0
$697$	19.4554			0.736928
$698$		0			0
$699$	−2.99402	−	5.18580i	−0.113244	−	0.196145i
$700$		0			0
$701$	−1.87303	−	3.24418i	−0.0707433	−	0.122531i	0.828484	−	0.560013i	$-0.189204\pi$
$701$	−1.87303	−	3.24418i	−0.0707433	−	0.122531i	−0.899227	+	0.437482i	$0.855870\pi$
$702$		0			0
$703$	−10.1223	−	17.5323i	−0.381769	−	0.661244i
$704$		0			0
$705$	3.40947	+	5.90538i	0.128408	+	0.222409i
$706$		0			0
$707$	14.5365	−	25.1780i	0.546703	−	0.946917i
$708$		0			0
$709$	24.3008	−	42.0903i	0.912637	−	1.58073i	0.102312	−	0.994752i	$-0.467376\pi$
$709$	24.3008	−	42.0903i	0.912637	−	1.58073i	0.810325	−	0.585981i	$-0.199291\pi$
$710$		0			0
$711$	−5.84670	−	10.1268i	−0.219268	−	0.379784i
$712$		0			0
$713$	−9.15849			−0.342988
$714$		0			0
$715$	6.27047			0.234502
$716$		0			0
$717$	−10.4991	−	18.1850i	−0.392097	−	0.679131i
$718$		0			0
$719$	22.0646	−	38.2171i	0.822872	−	1.42526i	−0.0806630	−	0.996741i	$-0.525704\pi$
$719$	22.0646	−	38.2171i	0.822872	−	1.42526i	0.903535	−	0.428514i	$-0.140963\pi$
$720$		0			0
$721$	−12.1225	+	20.9968i	−0.451467	+	0.781963i
$722$		0			0
$723$	13.6890			0.509098
$724$		0			0
$725$	0.387293	+	0.670812i	0.0143837	+	0.0249133i
$726$		0			0
$727$	4.70643	−	8.15177i	0.174552	−	0.302332i	−0.765454	−	0.643490i	$-0.777486\pi$
$727$	4.70643	−	8.15177i	0.174552	−	0.302332i	0.940006	+	0.341158i	$0.110819\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	7.24250	−	12.5444i	0.267874	−	0.463971i
$732$		0			0
$733$	6.14522	+	10.6438i	0.226979	+	0.393139i	0.956911	−	0.290380i	$-0.0937818\pi$
$733$	6.14522	+	10.6438i	0.226979	+	0.393139i	−0.729932	+	0.683519i	$0.760448\pi$
$734$		0			0
$735$	−6.03327	+	10.4499i	−0.222540	+	0.385451i
$736$		0			0
$737$	−5.63407	−	11.3534i	−0.207534	−	0.418207i
$738$		0			0
$739$	−7.70943	+	13.3531i	−0.283596	+	0.491203i	−0.972268	−	0.233870i	$-0.924861\pi$
$739$	−7.70943	+	13.3531i	−0.283596	+	0.491203i	0.688672	+	0.725073i	$0.258194\pi$
$740$		0			0
$741$	8.13862	+	14.0965i	0.298980	+	0.517848i
$742$		0			0
$743$	19.0137	−	32.9327i	0.697545	−	1.20818i	−0.271770	−	0.962362i	$-0.587609\pi$
$743$	19.0137	−	32.9327i	0.697545	−	1.20818i	0.969315	−	0.245821i	$-0.0790576\pi$
$744$		0			0
$745$	−12.9091			−0.472952
$746$		0			0
$747$	5.02913	−	8.71071i	0.184006	−	0.318708i
$748$		0			0
$749$	14.2312	+	24.6492i	0.519998	+	0.900663i
$750$		0			0
$751$	−5.42821			−0.198078			−0.0990391	−	0.995084i	$-0.531577\pi$
$751$	−5.42821			−0.198078			−0.0990391	+	0.995084i	$0.531577\pi$
$752$		0			0
$753$	−2.93590	+	5.08513i	−0.106990	+	0.185313i
$754$		0			0
$755$	−1.79380	+	3.10695i	−0.0652830	+	0.113073i
$756$		0			0
$757$	−18.1748	−	31.4796i	−0.660573	−	1.14415i	−0.980465	−	0.196693i	$-0.936980\pi$
$757$	−18.1748	−	31.4796i	−0.660573	−	1.14415i	0.319892	−	0.947454i	$-0.396353\pi$
$758$		0			0
$759$	7.44977			0.270409
$760$		0			0
$761$	−11.2722			−0.408617			−0.204308	−	0.978907i	$-0.565494\pi$
$761$	−11.2722			−0.408617			−0.204308	+	0.978907i	$0.565494\pi$
$762$		0			0
$763$	33.1211	+	57.3674i	1.19906	+	2.07684i
$764$		0			0
$765$	−1.99263	+	3.45134i	−0.0720437	+	0.124783i
$766$		0			0
$767$	−18.2785	+	31.6593i	−0.659998	+	1.14315i
$768$		0			0
$769$	8.51281	+	14.7446i	0.306980	+	0.531705i	0.977700	−	0.210006i	$-0.0673482\pi$
$769$	8.51281	+	14.7446i	0.306980	+	0.531705i	−0.670720	+	0.741710i	$0.734015\pi$
$770$		0			0
$771$	−2.40142	−	4.15939i	−0.0864852	−	0.149797i
$772$		0			0
$773$	4.99794	+	8.65669i	0.179763	+	0.311359i	0.941799	−	0.336175i	$-0.109133\pi$
$773$	4.99794	+	8.65669i	0.179763	+	0.311359i	−0.762036	+	0.647535i	$0.775800\pi$
$774$		0			0
$775$	−0.951794	−	1.64856i	−0.0341895	−	0.0592179i
$776$		0			0
$777$	21.9924			0.788972
$778$		0			0
$779$	19.6226			0.703054
$780$		0			0
$781$	−7.99510	+	13.8479i	−0.286087	+	0.495518i
$782$		0			0
$783$	−0.387293	−	0.670812i	−0.0138407	−	0.0239729i
$784$		0			0
$785$	−0.0871390	+	0.150929i	−0.00311012	+	0.00538689i
$786$		0			0
$787$	5.85915	−	10.1483i	0.208856	−	0.361750i	−0.742498	−	0.669848i	$-0.766359\pi$
$787$	5.85915	−	10.1483i	0.208856	−	0.361750i	0.951354	+	0.308098i	$0.0996926\pi$
$788$		0			0
$789$	−8.03375			−0.286009
$790$		0			0
$791$	32.4660	−	56.2328i	1.15436	−	1.99941i
$792$		0			0
$793$	−9.91607	−	17.1751i	−0.352130	−	0.609907i
$794$		0			0
$795$	2.93977			0.104263
$796$		0			0
$797$	18.5711	+	32.1661i	0.657822	+	1.13938i	0.981178	+	0.193104i	$0.0618554\pi$
$797$	18.5711	+	32.1661i	0.657822	+	1.13938i	−0.323356	+	0.946277i	$0.604811\pi$
$798$		0			0
$799$	27.1753			0.961392
$800$		0			0
$801$	11.9973			0.423905
$802$		0			0
$803$	−6.06529			−0.214039
$804$		0			0
$805$	21.0081			0.740438
$806$		0			0
$807$	−20.5623			−0.723826
$808$		0			0
$809$	14.2583			0.501297			0.250648	−	0.968078i	$-0.419356\pi$
$809$	14.2583			0.501297			0.250648	+	0.968078i	$0.419356\pi$
$810$		0			0
$811$	−15.6411	−	27.0911i	−0.549232	−	0.951297i	−0.998327	−	0.0578135i	$-0.981587\pi$
$811$	−15.6411	−	27.0911i	−0.549232	−	0.951297i	0.449096	−	0.893484i	$-0.351746\pi$
$812$		0			0
$813$	18.9461			0.664467
$814$		0			0
$815$	−1.82908	−	3.16805i	−0.0640698	−	0.110972i
$816$		0			0
$817$	7.30474	−	12.6522i	0.255560	−	0.442644i
$818$		0			0
$819$	−17.6825			−0.617877
$820$		0			0
$821$	−17.2159	+	29.8188i	−0.600839	+	1.04068i	0.391856	+	0.920027i	$0.371833\pi$
$821$	−17.2159	+	29.8188i	−0.600839	+	1.04068i	−0.992694	+	0.120656i	$0.961500\pi$
$822$		0			0
$823$	−1.04769	+	1.81466i	−0.0365202	+	0.0632549i	−0.883708	−	0.468039i	$-0.844961\pi$
$823$	−1.04769	+	1.81466i	−0.0365202	+	0.0632549i	0.847188	+	0.531294i	$0.178294\pi$
$824$		0			0
$825$	0.774215	+	1.34098i	0.0269547	+	0.0466869i
$826$		0			0
$827$	−7.42881	+	12.8671i	−0.258325	+	0.447432i	−0.965793	−	0.259313i	$-0.916504\pi$
$827$	−7.42881	+	12.8671i	−0.258325	+	0.447432i	0.707468	+	0.706745i	$0.249837\pi$
$828$		0			0
$829$	9.92380			0.344668			0.172334	−	0.985039i	$-0.444869\pi$
$829$	9.92380			0.344668			0.172334	+	0.985039i	$0.444869\pi$
$830$		0			0
$831$	18.4595			0.640351
$832$		0			0
$833$	24.0441	+	41.6457i	0.833080	+	1.44294i
$834$		0			0
$835$	6.18346	+	10.7101i	0.213988	+	0.370637i
$836$		0			0
$837$	0.951794	+	1.64856i	0.0328988	+	0.0569824i
$838$		0			0
$839$	−5.40743	−	9.36595i	−0.186685	−	0.323348i	0.757458	−	0.652884i	$-0.226441\pi$
$839$	−5.40743	−	9.36595i	−0.186685	−	0.323348i	−0.944143	+	0.329536i	$0.893108\pi$
$840$		0			0
$841$	14.2000	−	24.5951i	0.489655	−	0.848108i
$842$		0			0
$843$	−1.81169	+	3.13794i	−0.0623980	+	0.108076i
$844$		0			0
$845$	1.69948	+	2.94358i	0.0584637	+	0.101262i
$846$		0			0
$847$	−37.5624			−1.29066
$848$		0			0
$849$	18.7679			0.644112
$850$		0			0
$851$	−12.1159	−	20.9854i	−0.415329	−	0.719371i
$852$		0			0
$853$	−12.1733	+	21.0848i	−0.416807	+	0.721931i	−0.995616	−	0.0935320i	$-0.970184\pi$
$853$	−12.1733	+	21.0848i	−0.416807	+	0.721931i	0.578809	+	0.815463i	$0.303518\pi$
$854$		0			0
$855$	−2.00975	+	3.48099i	−0.0687321	+	0.119047i
$856$		0			0
$857$	−29.9953			−1.02462			−0.512311	−	0.858800i	$-0.671210\pi$
$857$	−29.9953			−1.02462			−0.512311	+	0.858800i	$0.671210\pi$
$858$		0			0
$859$	7.21209	+	12.4917i	0.246073	+	0.426211i	0.962433	−	0.271520i	$-0.0875263\pi$
$859$	7.21209	+	12.4917i	0.246073	+	0.426211i	−0.716360	+	0.697731i	$0.754193\pi$
$860$		0			0
$861$	−10.6584	+	18.4608i	−0.363236	+	0.629143i
$862$		0			0
$863$	16.8312			0.572941			0.286470	−	0.958089i	$-0.407518\pi$
$863$	16.8312			0.572941			0.286470	+	0.958089i	$0.407518\pi$
$864$		0			0
$865$	5.13800	−	8.89928i	0.174697	−	0.302585i
$866$		0			0
$867$	−0.558854	−	0.967963i	−0.0189797	−	0.0328737i
$868$		0			0
$869$	−9.05321	+	15.6806i	−0.307109	+	0.531929i
$870$		0			0
$871$	18.3468	−	27.6066i	0.621658	−	0.935414i
$872$		0			0
$873$	0.0931549	−	0.161349i	0.00315282	−	0.00546084i
$874$		0			0
$875$	2.18326	+	3.78152i	0.0738077	+	0.127839i
$876$		0			0
$877$	24.1220	−	41.7805i	0.814542	−	1.41083i	−0.0951137	−	0.995466i	$-0.530321\pi$
$877$	24.1220	−	41.7805i	0.814542	−	1.41083i	0.909656	−	0.415362i	$-0.136345\pi$
$878$		0			0
$879$	−14.6838			−0.495274
$880$		0			0
$881$	3.65905	−	6.33765i	0.123276	−	0.213521i	−0.797781	−	0.602947i	$-0.793993\pi$
$881$	3.65905	−	6.33765i	0.123276	−	0.213521i	0.921058	+	0.389426i	$0.127326\pi$
$882$		0			0
$883$	−4.97113	−	8.61025i	−0.167292	−	0.289758i	0.770175	−	0.637833i	$-0.220169\pi$
$883$	−4.97113	−	8.61025i	−0.167292	−	0.289758i	−0.937467	+	0.348075i	$0.886836\pi$
$884$		0			0
$885$	−9.02740			−0.303453
$886$		0			0
$887$	23.0074	−	39.8500i	0.772513	−	1.33803i	−0.163669	−	0.986515i	$-0.552333\pi$
$887$	23.0074	−	39.8500i	0.772513	−	1.33803i	0.936182	−	0.351516i	$-0.114334\pi$
$888$		0			0
$889$	10.3687	−	17.9591i	0.347755	−	0.602330i
$890$		0			0
$891$	−0.774215	−	1.34098i	−0.0259372	−	0.0449245i
$892$		0			0
$893$	27.4088			0.917200
$894$		0			0
$895$	−4.67334			−0.156212
$896$		0			0
$897$	9.74157	+	16.8729i	0.325262	+	0.563370i
$898$		0			0
$899$	0.737247	−	1.27695i	0.0245886	−	0.0425886i
$900$		0			0
$901$	5.85787	−	10.1461i	0.195154	−	0.338016i
$902$		0			0
$903$	7.93538	+	13.7445i	0.264073	+	0.457388i
$904$		0			0
$905$	8.86171	+	15.3489i	0.294573	+	0.510216i
$906$		0			0
$907$	−5.90469	−	10.2272i	−0.196062	−	0.339590i	0.751186	−	0.660091i	$-0.229482\pi$
$907$	−5.90469	−	10.2272i	−0.196062	−	0.339590i	−0.947248	+	0.320501i	$0.896149\pi$
$908$		0			0
$909$	3.32909	+	5.76615i	0.110419	+	0.191251i
$910$		0			0
$911$	−35.6124			−1.17989			−0.589946	−	0.807443i	$-0.700851\pi$
$911$	−35.6124			−1.17989			−0.589946	+	0.807443i	$0.700851\pi$
$912$		0			0
$913$	−15.5745			−0.515441
$914$		0			0
$915$	2.44868	−	4.24123i	0.0809508	−	0.140211i
$916$		0			0
$917$	0.544215	+	0.942608i	0.0179716	+	0.0311277i
$918$		0			0
$919$	12.6492	−	21.9091i	0.417260	−	0.722716i	−0.578403	−	0.815751i	$-0.696324\pi$
$919$	12.6492	−	21.9091i	0.417260	−	0.722716i	0.995663	+	0.0930358i	$0.0296571\pi$
$920$		0			0
$921$	11.8768	−	20.5711i	0.391353	−	0.677842i
$922$		0			0
$923$	−41.8187			−1.37648
$924$		0			0
$925$	2.51829	−	4.36181i	0.0828010	−	0.143415i
$926$		0			0
$927$	−2.77624	−	4.80859i	−0.0911838	−	0.157935i
$928$		0			0
$929$	−9.73268			−0.319319			−0.159659	−	0.987172i	$-0.551040\pi$
$929$	−9.73268			−0.319319			−0.159659	+	0.987172i	$0.551040\pi$
$930$		0			0
$931$	24.2508	+	42.0035i	0.794786	+	1.37661i
$932$		0			0
$933$	1.63955			0.0536765
$934$		0			0
$935$	6.17090			0.201810
$936$		0			0
$937$	4.31111			0.140838			0.0704189	−	0.997518i	$-0.477566\pi$
$937$	4.31111			0.140838			0.0704189	+	0.997518i	$0.477566\pi$
$938$		0			0
$939$	1.62336			0.0529762
$940$		0			0
$941$	37.9298			1.23648			0.618239	−	0.785990i	$-0.287846\pi$
$941$	37.9298			1.23648			0.618239	+	0.785990i	$0.287846\pi$
$942$		0			0
$943$	23.4874			0.764856
$944$		0			0
$945$	−2.18326	−	3.78152i	−0.0710215	−	0.123013i
$946$		0			0
$947$	12.9093			0.419496			0.209748	−	0.977755i	$-0.432736\pi$
$947$	12.9093			0.419496			0.209748	+	0.977755i	$0.432736\pi$
$948$		0			0
$949$	−7.93118	−	13.7372i	−0.257457	−	0.445929i
$950$		0			0
$951$	8.96536	−	15.5285i	0.290722	−	0.503545i
$952$		0			0
$953$	51.3493			1.66337			0.831684	−	0.555249i	$-0.187377\pi$
$953$	51.3493			1.66337			0.831684	+	0.555249i	$0.187377\pi$
$954$		0			0
$955$	−2.71018	+	4.69417i	−0.0876994	+	0.151900i
$956$		0			0
$957$	−0.599697	+	1.03871i	−0.0193854	+	0.0335766i
$958$		0			0
$959$	35.8774	+	62.1415i	1.15854	+	2.00665i
$960$		0			0
$961$	13.6882	−	23.7086i	0.441554	−	0.764794i
$962$		0			0
$963$	−6.51834			−0.210050
$964$		0			0
$965$	−9.93928			−0.319957
$966$		0			0
$967$	−2.96302	−	5.13210i	−0.0952842	−	0.165037i	0.814443	−	0.580244i	$-0.197043\pi$
$967$	−2.96302	−	5.13210i	−0.0952842	−	0.165037i	−0.909727	+	0.415206i	$0.863709\pi$
$968$		0			0
$969$	8.00938	+	13.8727i	0.257299	+	0.445654i
$970$		0			0
$971$	1.63899	+	2.83881i	0.0525976	+	0.0911017i	0.891125	−	0.453757i	$-0.149917\pi$
$971$	1.63899	+	2.83881i	0.0525976	+	0.0911017i	−0.838528	+	0.544859i	$0.816583\pi$
$972$		0			0
$973$	18.7999	+	32.5623i	0.602696	+	1.04390i
$974$		0			0
$975$	−2.02478	+	3.50702i	−0.0648449	+	0.112315i
$976$		0			0
$977$	6.20100	−	10.7405i	0.198388	−	0.343617i	−0.749618	−	0.661871i	$-0.769763\pi$
$977$	6.20100	−	10.7405i	0.198388	−	0.343617i	0.948006	+	0.318253i	$0.103096\pi$
$978$		0			0
$979$	−9.28853	−	16.0882i	−0.296863	−	0.514181i
$980$		0			0
$981$	−15.1705			−0.484355
$982$		0			0
$983$	0.768429			0.0245091			0.0122545	−	0.999925i	$-0.496099\pi$
$983$	0.768429			0.0245091			0.0122545	+	0.999925i	$0.496099\pi$
$984$		0			0
$985$	−0.490545	−	0.849650i	−0.0156301	−	0.0270721i
$986$		0			0
$987$	−14.8875	+	25.7860i	−0.473876	+	0.820777i
$988$		0			0
$989$	8.74345	−	15.1441i	0.278026	−	0.481554i
$990$		0			0
$991$	−8.87346			−0.281875			−0.140937	−	0.990019i	$-0.545012\pi$
$991$	−8.87346			−0.281875			−0.140937	+	0.990019i	$0.545012\pi$
$992$		0			0
$993$	3.99055	+	6.91184i	0.126636	+	0.219341i
$994$		0			0
$995$	1.34262	−	2.32548i	0.0425638	−	0.0737227i
$996$		0			0
$997$	43.4055			1.37467			0.687333	−	0.726342i	$-0.258781\pi$
$997$	43.4055			1.37467			0.687333	+	0.726342i	$0.258781\pi$
$998$		0			0
$999$	−2.51829	+	4.36181i	−0.0796753	+	0.138002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.3781.1	yes	22
67.37	even	3	inner	4020.2.q.l.841.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.1	✓	22	67.37	even	3	inner
4020.2.q.l.3781.1	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-2.18326 - 3.78152i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-2.18326 - 3.78152i) q^{7} +1.00000 q^{9} +(-0.774215 - 1.34098i) q^{11} +(2.02478 - 3.50702i) q^{13} +1.00000 q^{15} +(1.99263 - 3.45134i) q^{17} +(2.00975 - 3.48099i) q^{19} +(2.18326 + 3.78152i) q^{21} +(2.40559 - 4.16660i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.387293 + 0.670812i) q^{29} +(-0.951794 - 1.64856i) q^{31} +(0.774215 + 1.34098i) q^{33} +(2.18326 + 3.78152i) q^{35} +(2.51829 - 4.36181i) q^{37} +(-2.02478 + 3.50702i) q^{39} +(2.44093 + 4.22781i) q^{41} +3.63465 q^{43} -1.00000 q^{45} +(3.40947 + 5.90538i) q^{47} +(-6.03327 + 10.4499i) q^{49} +(-1.99263 + 3.45134i) q^{51} +2.93977 q^{53} +(0.774215 + 1.34098i) q^{55} +(-2.00975 + 3.48099i) q^{57} -9.02740 q^{59} +(2.44868 - 4.24123i) q^{61} +(-2.18326 - 3.78152i) q^{63} +(-2.02478 + 3.50702i) q^{65} +(8.16914 + 0.514996i) q^{67} +(-2.40559 + 4.16660i) q^{69} +(-5.16336 - 8.94320i) q^{71} +(1.95853 - 3.39227i) q^{73} -1.00000 q^{75} +(-3.38063 + 5.85542i) q^{77} +(-5.84670 - 10.1268i) q^{79} +1.00000 q^{81} +(5.02913 - 8.71071i) q^{83} +(-1.99263 + 3.45134i) q^{85} +(-0.387293 - 0.670812i) q^{87} +11.9973 q^{89} -17.6825 q^{91} +(0.951794 + 1.64856i) q^{93} +(-2.00975 + 3.48099i) q^{95} +(0.0931549 - 0.161349i) q^{97} +(-0.774215 - 1.34098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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